There was a moment, as the pressure was straying dangerously close towards intolerable, when Roy Hodgson could be seen yanking at his collar, desperately trying to loosen the knot of his tie. It was that kind of night, full of anxiety and drama and plenty of danger, until, finally, Steven Gerrard made sure all the pent-up emotion could be released.

His goal typified everything Gerrard stands for, riding a couple of challenges, refusing to give up on the ball, absolutely determined to have the final touch despite the close proximity of so many defenders. Gerrard has scarcely celebrated a goal with more joy and that was the moment, after all the fretting and nervous tension, that England knew their block-booking at the five-star hotel in Rio next June was safe. At last, they could relax.

Roy Hodgson's team had toyed with everyone's nerves. They had come across a Poland side that gave everything on a night when Wembley often sounded more like Warsaw, and Gerrard's late, decisive strike came at a stage of the night when England's management was thinking about little more than protecting Wayne Rooney's first-half goal.

Jack Wilshere, a midfielder, had been brought on for Daniel Sturridge, a striker. James Milner was on for Andros Townsend and Rooney had started to drop back to the centre-circle. Everyone knew the plan. Or at least everyone bar the man wearing the captain's armband. Gerrard plainly had other ideas as he set off on that final, driving run into the opposition penalty area, slaloming between Kamil Glik and Grzegorz Wojtkowiak and getting his shot away as a third defender, Artur Jedzejczyk, and the goalkeeper, Wojciech Szczesny, tried to close him out.

It was a goal that brought a burst of euphoria inside Wembley that continued after the final whistle. Euphoria and relief. England have made heavy going of Group H but they have handled the pressures of their last two games admirably and playing at their own stadium no longer appears to fill with them with apprehension.

They also had to see off a side that frequently gave the impression they were playing above themselves. Poland might be languishing 65th in Fifa's world rankings, two places below Scotland, but it quickly became apparent, just as England had feared, this was a team that would rise to the challenge of playing at Wembley.

Waldemar Fornalik's side had phenomenal backing from their raucous, beery, fire-cracking supporters. Along the way, there was another backdrop to this match, in the form of the goal updates from Serravalle informing everyone that Ukraine were on their way to the obligatory walkover against San Marino. England had known they would almost certainly have to win. For long spells, the tension was extreme.

Poland played with great energy, quick to the ball, strong in the challenge, and projecting the clear sense they had absolutely no intention whatsoever of making this a straightforward night. Hodgson talked about England's attacking being "spectacular" in the first half but what a different occasion it might have been if Robert Lewandowski had taken either of his two chances to open the scoring in the opening 25 minutes. At times, England subjected their opponents to ferocious pressure without being able to kill them off. In other moments, they looked vulnerable. Put together, it made for a nerve-shredding occasion.

Rooney's goal certainly came at a good time as the news filtered through that Ukraine were making light work of San Marino. Leighton Baines, playing with distinction again, sent over a left-wing cross with pace and accuracy. Welbeck, prominently involved all night, could not reach it but Rooney was directly behind him, flashing his header past Szczesny.

By that stage Townsend, playing again as though immune to any form of nerves, had curled a lovely, left-footed effort against the crossbar and Welbeck had slashed a shot wide from a position when he really should have done better. Yet Poland could also look back on more than one moment in the opening 45 minutes when the entire complexion of the night could conceivably have changed.

At one point early on Szczesny, playing because of an injury to Artur Boruc, left his goal-line to catch Baines's corner and then rolled the ball out to Lewandowski on the edge of his penalty area. What followed was extraordinary. Lewandowski simply ran and ran. His shot was struck too close to Joe Hart but it was alarming to see him make it unchallenged from one penalty area to the other.

His best chance came midway through the first half when England were caught on the counterattack again. Jakub Blaszczykowski's dummy was a wonderful piece of improvisation and suddenly Lewandowski, the player England feared the most, was bearing down on goal, dragging his shot wide. There were more anxious moments to come after the break.

Mateusz Klich, a half-time substitute, almost equalised with his first touch, courtesy of a deflection off Gary Cahill. Hart had to dash from his goal-line to thwart Lewandowski and, around the hour mark, England were starting to look edgy once again. Overall, however, Cahill and Phil Jagielka, aided and abetted by Baines and Chris Smalling, protected Hart well.

Hodgson was right, too, when he said that on the balance of play England had deserved the win, but it was a close-run thing at times and they desperately wanted that second goal to lift all the gathering anxiety. Gerrard delivered it and England, amid scenes of great jubilation, could start looking forward to Brazil.